In [259]:
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import scipy.stats as st
import statsmodels.stats as sm
import sklearn
In [190]:
pd.set_option('display.max_rows',500)
pd.set_option('display.max_columns',100)
pd.set_option('display.width',500)
In [160]:
df= pd.read_csv('kc_housingdata.csv')
In [161]:
df.shape
Out[161]:
(21613, 21)
In [162]:
df.head()
Out[162]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view ... grade sqft_above sqft_basement yr_built yr_renovated zipcode lat long sqft_living15 sqft_lot15
0 7129300520 20141013T000000 221900.0 3 1.00 1180 5650 1.0 0 0 ... 7 1180 0 1955 0 98178 47.5112 -122.257 1340 5650
1 6414100192 20141209T000000 538000.0 3 2.25 2570 7242 2.0 0 0 ... 7 2170 400 1951 1991 98125 47.7210 -122.319 1690 7639
2 5631500400 20150225T000000 180000.0 2 1.00 770 10000 1.0 0 0 ... 6 770 0 1933 0 98028 47.7379 -122.233 2720 8062
3 2487200875 20141209T000000 604000.0 4 3.00 1960 5000 1.0 0 0 ... 7 1050 910 1965 0 98136 47.5208 -122.393 1360 5000
4 1954400510 20150218T000000 510000.0 3 2.00 1680 8080 1.0 0 0 ... 8 1680 0 1987 0 98074 47.6168 -122.045 1800 7503

5 rows × 21 columns

In [163]:
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21613 entries, 0 to 21612
Data columns (total 21 columns):
 #   Column         Non-Null Count  Dtype  
---  ------         --------------  -----  
 0   id             21613 non-null  int64  
 1   date           21613 non-null  object 
 2   price          21613 non-null  float64
 3   bedrooms       21613 non-null  int64  
 4   bathrooms      21613 non-null  float64
 5   sqft_living    21613 non-null  int64  
 6   sqft_lot       21613 non-null  int64  
 7   floors         21613 non-null  float64
 8   waterfront     21613 non-null  int64  
 9   view           21613 non-null  int64  
 10  condition      21613 non-null  int64  
 11  grade          21613 non-null  int64  
 12  sqft_above     21613 non-null  int64  
 13  sqft_basement  21613 non-null  int64  
 14  yr_built       21613 non-null  int64  
 15  yr_renovated   21613 non-null  int64  
 16  zipcode        21613 non-null  int64  
 17  lat            21613 non-null  float64
 18  long           21613 non-null  float64
 19  sqft_living15  21613 non-null  int64  
 20  sqft_lot15     21613 non-null  int64  
dtypes: float64(5), int64(15), object(1)
memory usage: 3.5+ MB

image.png

In [ ]:
df.drop('id',axis=1,inplace=True)
In [164]:
df.yr_renovated.value_counts(normalize=True)
Out[164]:
0       0.957711
2014    0.004210
2013    0.001712
2003    0.001666
2005    0.001619
          ...   
1951    0.000046
1959    0.000046
1948    0.000046
1954    0.000046
1944    0.000046
Name: yr_renovated, Length: 70, dtype: float64
In [165]:
def year(x):
    if x==0: return 0
    if x!=0: return 1  
df['renovated_status']=df.yr_renovated.apply(year)
In [192]:
df.head()
Out[192]:
date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade sqft_above sqft_basement yr_built yr_renovated zipcode lat long sqft_living15 sqft_lot15 renovated_status building_age current_yr house_age
0 2014-10-13 221900.0 3 1.00 1180 5650 1.0 0 0 3 7 1180 0 1955 0 98178 47.5112 -122.257 1340 5650 0 59 2014 59
1 2014-12-09 538000.0 3 2.25 2570 7242 2.0 0 0 3 7 2170 400 1951 1991 98125 47.7210 -122.319 1690 7639 1 63 2014 63
2 2015-02-25 180000.0 2 1.00 770 10000 1.0 0 0 3 6 770 0 1933 0 98028 47.7379 -122.233 2720 8062 0 82 2015 82
3 2014-12-09 604000.0 4 3.00 1960 5000 1.0 0 0 5 7 1050 910 1965 0 98136 47.5208 -122.393 1360 5000 0 49 2014 49
4 2015-02-18 510000.0 3 2.00 1680 8080 1.0 0 0 3 8 1680 0 1987 0 98074 47.6168 -122.045 1800 7503 0 28 2015 28
In [ ]:
In [ ]:
In [193]:
df.columns
Out[193]:
Index(['date', 'price', 'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'waterfront', 'view', 'condition', 'grade', 'sqft_above', 'sqft_basement', 'yr_built', 'yr_renovated', 'zipcode', 'lat', 'long', 'sqft_living15', 'sqft_lot15', 'renovated_status', 'building_age', 'current_yr', 'house_age'], dtype='object')
In [195]:
df.shape
Out[195]:
(21613, 19)
In [196]:
df.head()
Out[196]:
price bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade sqft_above sqft_basement zipcode lat long sqft_living15 sqft_lot15 renovated_status house_age
0 221900.0 3 1.00 1180 5650 1.0 0 0 3 7 1180 0 98178 47.5112 -122.257 1340 5650 0 59
1 538000.0 3 2.25 2570 7242 2.0 0 0 3 7 2170 400 98125 47.7210 -122.319 1690 7639 1 63
2 180000.0 2 1.00 770 10000 1.0 0 0 3 6 770 0 98028 47.7379 -122.233 2720 8062 0 82
3 604000.0 4 3.00 1960 5000 1.0 0 0 5 7 1050 910 98136 47.5208 -122.393 1360 5000 0 49
4 510000.0 3 2.00 1680 8080 1.0 0 0 3 8 1680 0 98074 47.6168 -122.045 1800 7503 0 28
In [189]:
df.head()
Out[189]:
date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition ... yr_renovated zipcode lat long sqft_living15 sqft_lot15 renovated_status building_age current_yr house_age
0 2014-10-13 221900.0 3 1.00 1180 5650 1.0 0 0 3 ... 0 98178 47.5112 -122.257 1340 5650 0 59 2014 59
1 2014-12-09 538000.0 3 2.25 2570 7242 2.0 0 0 3 ... 1991 98125 47.7210 -122.319 1690 7639 1 63 2014 63
2 2015-02-25 180000.0 2 1.00 770 10000 1.0 0 0 3 ... 0 98028 47.7379 -122.233 2720 8062 0 82 2015 82
3 2014-12-09 604000.0 4 3.00 1960 5000 1.0 0 0 5 ... 0 98136 47.5208 -122.393 1360 5000 0 49 2014 49
4 2015-02-18 510000.0 3 2.00 1680 8080 1.0 0 0 3 ... 0 98074 47.6168 -122.045 1800 7503 0 28 2015 28

5 rows × 24 columns

Data Understanding¶

In [ ]:

Descriptive analytics¶

In [198]:
df.describe().apply(lambda s:s.apply('{0:6f}'.format))
Out[198]:
price bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade sqft_above sqft_basement zipcode lat long sqft_living15 sqft_lot15 renovated_status house_age
count 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000 21613.000000
mean 540088.141767 3.370842 2.114757 2079.899736 15106.967566 1.494309 0.007542 0.234303 3.409430 7.656873 1788.390691 291.509045 98077.939805 47.560053 -122.213896 1986.552492 12768.455652 0.042289 43.317818
std 367127.196483 0.930062 0.770163 918.440897 41420.511515 0.539989 0.086517 0.766318 0.650743 1.175459 828.090978 442.575043 53.505026 0.138564 0.140828 685.391304 27304.179631 0.201253 29.375493
min 75000.000000 0.000000 0.000000 290.000000 520.000000 1.000000 0.000000 0.000000 1.000000 1.000000 290.000000 0.000000 98001.000000 47.155900 -122.519000 399.000000 651.000000 0.000000 -1.000000
25% 321950.000000 3.000000 1.750000 1427.000000 5040.000000 1.000000 0.000000 0.000000 3.000000 7.000000 1190.000000 0.000000 98033.000000 47.471000 -122.328000 1490.000000 5100.000000 0.000000 18.000000
50% 450000.000000 3.000000 2.250000 1910.000000 7618.000000 1.500000 0.000000 0.000000 3.000000 7.000000 1560.000000 0.000000 98065.000000 47.571800 -122.230000 1840.000000 7620.000000 0.000000 40.000000
75% 645000.000000 4.000000 2.500000 2550.000000 10688.000000 2.000000 0.000000 0.000000 4.000000 8.000000 2210.000000 560.000000 98118.000000 47.678000 -122.125000 2360.000000 10083.000000 0.000000 63.000000
max 7700000.000000 33.000000 8.000000 13540.000000 1651359.000000 3.500000 1.000000 4.000000 5.000000 13.000000 9410.000000 4820.000000 98199.000000 47.777600 -121.315000 6210.000000 871200.000000 1.000000 115.000000
In [168]:
sns.boxplot(y=df.price)
Out[168]:
<AxesSubplot:ylabel='price'>
In [169]:
sns.distplot(df.price)

C:\Users\mallikarjunad\Anaconda3\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
Out[169]:
<AxesSubplot:xlabel='price', ylabel='Density'>

The price distribuition is right skewed. the mean of th hous price is more than the median. there are lot of houses on higher prices.

In [170]:
df.condition.value_counts()
Out[170]:
3    14031
4     5679
5     1701
2      172
1       30
Name: condition, dtype: int64
In [171]:
df.waterfront.value_counts()
Out[171]:
0    21450
1      163
Name: waterfront, dtype: int64
In [172]:
df.view.value_counts()
Out[172]:
0    19489
2      963
3      510
1      332
4      319
Name: view, dtype: int64
In [173]:
df.grade.value_counts(normalize=True)*100
Out[173]:
7     41.553695
8     28.075695
9     12.099200
6      9.429510
10     5.246842
11     1.846111
5      1.119696
12     0.416416
4      0.134179
13     0.060149
3      0.013881
1      0.004627
Name: grade, dtype: float64
In [199]:
df.columns
Out[199]:
Index(['price', 'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'waterfront', 'view', 'condition', 'grade', 'sqft_above', 'sqft_basement', 'zipcode', 'lat', 'long', 'sqft_living15', 'sqft_lot15', 'renovated_status', 'house_age'], dtype='object')
In [175]:
current_yr= pd.to_datetime(df.date)
df['current_yr']= pd.DatetimeIndex(current_yr).year
df['house_age'] = df.current_yr - df.yr_built
In [182]:
df.head()
Out[182]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view ... yr_built yr_renovated zipcode lat long sqft_living15 sqft_lot15 renovated_status building_age current_yr
0 7129300520 20141013T000000 221900.0 3 1.00 1180 5650 1.0 0 0 ... 1955 0 98178 47.5112 -122.257 1340 5650 0 59 2014
1 6414100192 20141209T000000 538000.0 3 2.25 2570 7242 2.0 0 0 ... 1951 1991 98125 47.7210 -122.319 1690 7639 1 63 2014
2 5631500400 20150225T000000 180000.0 2 1.00 770 10000 1.0 0 0 ... 1933 0 98028 47.7379 -122.233 2720 8062 0 82 2015
3 2487200875 20141209T000000 604000.0 4 3.00 1960 5000 1.0 0 0 ... 1965 0 98136 47.5208 -122.393 1360 5000 0 49 2014
4 1954400510 20150218T000000 510000.0 3 2.00 1680 8080 1.0 0 0 ... 1987 0 98074 47.6168 -122.045 1800 7503 0 28 2015

5 rows × 24 columns

In [142]:
df.head()
Out[142]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view ... sqft_basement yr_built yr_renovated zipcode lat long sqft_living15 sqft_lot15 renovated_status overall_age
0 7129300520 2014-10-13 221900.0 3 1.00 1180 5650 1.0 0 0 ... 0 1970-01-01 00:00:00.000001955 0 98178 47.5112 -122.257 1340 5650 0 16355 days 23:59:59.999998045
1 6414100192 2014-12-09 538000.0 3 2.25 2570 7242 2.0 0 0 ... 400 1970-01-01 00:00:00.000001951 1991 98125 47.7210 -122.319 1690 7639 1 16412 days 23:59:59.999998049
2 5631500400 2015-02-25 180000.0 2 1.00 770 10000 1.0 0 0 ... 0 1970-01-01 00:00:00.000001933 0 98028 47.7379 -122.233 2720 8062 0 16490 days 23:59:59.999998067
3 2487200875 2014-12-09 604000.0 4 3.00 1960 5000 1.0 0 0 ... 910 1970-01-01 00:00:00.000001965 0 98136 47.5208 -122.393 1360 5000 0 16412 days 23:59:59.999998035
4 1954400510 2015-02-18 510000.0 3 2.00 1680 8080 1.0 0 0 ... 0 1970-01-01 00:00:00.000001987 0 98074 47.6168 -122.045 1800 7503 0 16483 days 23:59:59.999998013

5 rows × 23 columns

In [200]:
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21613 entries, 0 to 21612
Data columns (total 19 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   price             21613 non-null  float64
 1   bedrooms          21613 non-null  int64  
 2   bathrooms         21613 non-null  float64
 3   sqft_living       21613 non-null  int64  
 4   sqft_lot          21613 non-null  int64  
 5   floors            21613 non-null  float64
 6   waterfront        21613 non-null  int64  
 7   view              21613 non-null  int64  
 8   condition         21613 non-null  int64  
 9   grade             21613 non-null  int64  
 10  sqft_above        21613 non-null  int64  
 11  sqft_basement     21613 non-null  int64  
 12  zipcode           21613 non-null  int64  
 13  lat               21613 non-null  float64
 14  long              21613 non-null  float64
 15  sqft_living15     21613 non-null  int64  
 16  sqft_lot15        21613 non-null  int64  
 17  renovated_status  21613 non-null  int64  
 18  house_age         21613 non-null  int64  
dtypes: float64(5), int64(14)
memory usage: 3.1 MB

4 groups:

Groups 1 & 3: convert renovated age as numeric keeping 0 as yr built

Group2 2 & 4: conver renovated yr as a categorical , keep 0 as 0 and the remaining values as 1

In [201]:
sns.pairplot(df)
Out[201]:
<seaborn.axisgrid.PairGrid at 0x1b9c8f61610>
In [194]:
df.drop(['date','yr_built', 'yr_renovated','building_age','current_yr'],axis=1, inplace=True)
In [208]:
plt.figure.figsize=(10,15)
In [282]:
plt.figure(figsize=(12,15))
sns.heatmap(df.corr()>0.5, annot=True)
Out[282]:
<AxesSubplot:>

Scaling :

In [215]:
from sklearn.preprocessing import RobustScaler
rs = RobustScaler()
In [216]:
df.columns
Out[216]:
Index(['price', 'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'waterfront', 'view', 'condition', 'grade', 'sqft_above', 'sqft_basement', 'zipcode', 'lat', 'long', 'sqft_living15', 'sqft_lot15', 'renovated_status', 'house_age'], dtype='object')
In [217]:
num_col= ['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 
          'sqft_above', 'sqft_basement', 'zipcode', 'lat', 'long', 'sqft_living15', 
          'sqft_lot15', 'house_age']
In [218]:
dfn= df.copy()
In [219]:
dfn.head()
Out[219]:
price bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade sqft_above sqft_basement zipcode lat long sqft_living15 sqft_lot15 renovated_status house_age
0 221900.0 3 1.00 1180 5650 1.0 0 0 3 7 1180 0 98178 47.5112 -122.257 1340 5650 0 59
1 538000.0 3 2.25 2570 7242 2.0 0 0 3 7 2170 400 98125 47.7210 -122.319 1690 7639 1 63
2 180000.0 2 1.00 770 10000 1.0 0 0 3 6 770 0 98028 47.7379 -122.233 2720 8062 0 82
3 604000.0 4 3.00 1960 5000 1.0 0 0 5 7 1050 910 98136 47.5208 -122.393 1360 5000 0 49
4 510000.0 3 2.00 1680 8080 1.0 0 0 3 8 1680 0 98074 47.6168 -122.045 1800 7503 0 28
In [221]:
for i in num_col:
    dfn[i]= rs.fit_transform(dfn[i].values.reshape(-1,1))
In [222]:
dfn.head()
Out[222]:
price bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade sqft_above sqft_basement zipcode lat long sqft_living15 sqft_lot15 renovated_status house_age
0 221900.0 0.0 -1.666667 -0.650045 -0.348442 -0.5 0 0 3 7 -0.372549 0.000000 1.329412 -0.292754 -0.133005 -0.574713 -0.395344 0 0.422222
1 538000.0 0.0 0.000000 0.587711 -0.066572 0.5 0 0 3 7 0.598039 0.714286 0.705882 0.720773 -0.438424 -0.172414 0.003813 1 0.511111
2 180000.0 -1.0 -1.666667 -1.015138 0.421742 -0.5 0 0 3 6 -0.774510 0.000000 -0.435294 0.802415 -0.014778 1.011494 0.088702 0 0.933333
3 604000.0 1.0 1.000000 0.044524 -0.463527 -0.5 0 0 5 7 -0.500000 1.625000 0.835294 -0.246377 -0.802956 -0.551724 -0.525788 0 0.200000
4 510000.0 0.0 -0.333333 -0.204809 0.081799 -0.5 0 0 3 8 0.117647 0.000000 0.105882 0.217391 0.911330 -0.045977 -0.023480 0 -0.266667

Segregation of Target variable and Features¶

In [223]:
x= dfn.drop('price', axis=1)
y= dfn.price
In [224]:
from sklearn.model_selection import train_test_split
In [238]:
x_train,x_test,y_train,y_test= train_test_split(x,y,test_size=0.2, random_state=12)
In [239]:
x_train.shape
Out[239]:
(17290, 18)
In [240]:
x_test.shape
Out[240]:
(4323, 18)
In [241]:
y_train.shape
Out[241]:
(17290,)
In [242]:
y_test.shape
Out[242]:
(4323,)
In [243]:
from sklearn.linear_model import LinearRegression
In [244]:
lin_model = LinearRegression()
model1_rs= lin_model.fit(x_train,y_train)
In [249]:
model1_rs.coef_
Out[249]:
array([-33734.90506239,  32034.22321263,  93755.54448154,   1355.68779146,
         3827.74723496, 611162.5648845 ,  52715.12667277,  26072.53294655,
        98135.50010388,  86735.07306659,  30031.61058007, -48721.71076849,
       123268.19116032, -44237.1522402 ,  23106.18922549,  -2299.95800152,
        32619.08076521, 116704.97695095])
In [251]:
model1_rs.score(x_train,y_train)
Out[251]:
0.7033294532015849
In [264]:
pred_y= model1_rs.predict(x_test)
In [265]:
pred_y
Out[265]:
array([278725.39740128, 104345.39202917, 261736.27883159, ...,
       424597.41030952, 499354.58992356, 765657.40092476])
In [266]:
y_test
Out[266]:
2019     275000.0
3435     279000.0
15940    200500.0
9811     750000.0
18665    395000.0
           ...   
3390     579000.0
6801     599000.0
4775     248500.0
10634    645000.0
1529     810000.0
Name: price, Length: 4323, dtype: float64
In [267]:
model1_rs.score(x_test,y_test)
Out[267]:
0.6865061731544676
In [257]:
from statsmodels.api import OLS
x_train = sm.add_constant(x_train)
model1_rs_ols= OLS(y_train,x_train).fit()
In [261]:
x_train.head()
Out[261]:
const bedrooms bathrooms sqft_living sqft_lot floors waterfront view condition grade sqft_above sqft_basement zipcode lat long sqft_living15 sqft_lot15 renovated_status house_age
20359 1.0 1.0 0.333333 0.088157 -0.498938 0.5 0 0 3 8 0.440196 0.0 0.317647 -1.513043 0.147783 -0.048276 -0.565924 0 -0.844444
10461 1.0 -1.0 0.333333 -0.596616 -1.075071 0.5 0 0 3 7 -0.313725 0.0 0.505882 -0.040580 -0.334975 -0.367816 -1.033915 0 -0.733333
20047 1.0 0.0 0.333333 0.623330 -0.064093 0.5 0 0 3 9 1.029412 0.0 -0.376471 0.595169 0.246305 0.885057 -0.083082 0 -0.888889
10581 1.0 -1.0 -1.666667 -0.997329 1.165368 -0.5 0 0 3 7 -0.754902 0.0 1.447059 -0.544928 -0.270936 -0.471264 0.477624 0 0.511111
17749 1.0 -1.0 -1.666667 -1.086376 -0.428116 -0.5 0 0 3 6 -0.852941 0.0 0.835294 -0.076329 -0.812808 -0.528736 -0.385310 0 1.266667
In [258]:
model1_rs_ols.summary()
Out[258]:
OLS Regression Results
Dep. Variable: price R-squared: 0.703
Model: OLS Adj. R-squared: 0.703
Method: Least Squares F-statistic: 2409.
Date: Sun, 12 Feb 2023 Prob (F-statistic): 0.00
Time: 11:17:18 Log-Likelihood: -2.3526e+05
No. Observations: 17290 AIC: 4.706e+05
Df Residuals: 17272 BIC: 4.707e+05
Df Model: 17
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -3.29e+05 1.88e+04 -17.528 0.000 -3.66e+05 -2.92e+05
bedrooms -3.373e+04 2045.246 -16.494 0.000 -3.77e+04 -2.97e+04
bathrooms 3.203e+04 2661.965 12.034 0.000 2.68e+04 3.73e+04
sqft_living 1.432e+05 2962.891 48.334 0.000 1.37e+05 1.49e+05
sqft_lot 1355.6878 301.348 4.499 0.000 765.015 1946.360
floors 3827.7472 3912.617 0.978 0.328 -3841.379 1.15e+04
waterfront 6.112e+05 1.91e+04 32.023 0.000 5.74e+05 6.49e+05
view 5.272e+04 2339.814 22.530 0.000 4.81e+04 5.73e+04
condition 2.607e+04 2571.834 10.138 0.000 2.1e+04 3.11e+04
grade 9.814e+04 2350.516 41.751 0.000 9.35e+04 1.03e+05
sqft_above 4.182e+04 3929.463 10.642 0.000 3.41e+04 4.95e+04
sqft_basement 5370.8033 2594.581 2.070 0.038 285.162 1.05e+04
zipcode -4.872e+04 3063.184 -15.906 0.000 -5.47e+04 -4.27e+04
lat 1.233e+05 2417.631 50.987 0.000 1.19e+05 1.28e+05
long -4.424e+04 2933.156 -15.082 0.000 -5e+04 -3.85e+04
sqft_living15 2.311e+04 3268.120 7.070 0.000 1.67e+04 2.95e+04
sqft_lot15 -2299.9580 418.314 -5.498 0.000 -3119.896 -1480.020
renovated_status 3.262e+04 7940.712 4.108 0.000 1.71e+04 4.82e+04
house_age 1.167e+05 3573.118 32.662 0.000 1.1e+05 1.24e+05
Omnibus: 13263.516 Durbin-Watson: 1.996
Prob(Omnibus): 0.000 Jarque-Bera (JB): 862677.421
Skew: 3.144 Prob(JB): 0.00
Kurtosis: 37.028 Cond. No. 4.97e+16


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 6.21e-28. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
In [260]:
st.f.sf(2409, 17,17272)
Out[260]:
0.0
In [269]:
import statsmodels.api as sm
x_test = sm.add_constant(x_test)
model1_rs_ols_test= OLS(y_test,x_test).fit()
model1_rs_ols_test.summary()
Out[269]:
OLS Regression Results
Dep. Variable: price R-squared: 0.696
Model: OLS Adj. R-squared: 0.695
Method: Least Squares F-statistic: 580.3
Date: Sun, 12 Feb 2023 Prob (F-statistic): 0.00
Time: 11:49:47 Log-Likelihood: -59235.
No. Observations: 4323 AIC: 1.185e+05
Df Residuals: 4305 BIC: 1.186e+05
Df Model: 17
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -2.696e+05 4.15e+04 -6.501 0.000 -3.51e+05 -1.88e+05
bedrooms -4.451e+04 4755.819 -9.359 0.000 -5.38e+04 -3.52e+04
bathrooms 2.991e+04 5919.237 5.054 0.000 1.83e+04 4.15e+04
sqft_living 1.696e+05 6468.168 26.221 0.000 1.57e+05 1.82e+05
sqft_lot -1551.1728 616.893 -2.514 0.012 -2760.601 -341.744
floors 1.906e+04 8796.600 2.167 0.030 1816.504 3.63e+04
waterfront 4.671e+05 4.08e+04 11.438 0.000 3.87e+05 5.47e+05
view 5.314e+04 5139.015 10.341 0.000 4.31e+04 6.32e+04
condition 2.586e+04 5622.285 4.600 0.000 1.48e+04 3.69e+04
grade 8.909e+04 5190.577 17.165 0.000 7.89e+04 9.93e+04
sqft_above 7.881e+04 8701.373 9.058 0.000 6.18e+04 9.59e+04
sqft_basement 2.807e+04 5611.103 5.003 0.000 1.71e+04 3.91e+04
zipcode -5.185e+04 6736.027 -7.698 0.000 -6.51e+04 -3.86e+04
lat 1.291e+05 5442.564 23.725 0.000 1.18e+05 1.4e+05
long -3.94e+04 6241.216 -6.312 0.000 -5.16e+04 -2.72e+04
sqft_living15 -329.0077 7315.060 -0.045 0.964 -1.47e+04 1.4e+04
sqft_lot15 -771.0594 755.147 -1.021 0.307 -2251.536 709.417
renovated_status 6.793e+04 1.78e+04 3.817 0.000 3.3e+04 1.03e+05
house_age 1.275e+05 7841.698 16.255 0.000 1.12e+05 1.43e+05
Omnibus: 4222.807 Durbin-Watson: 1.980
Prob(Omnibus): 0.000 Jarque-Bera (JB): 663551.884
Skew: 4.295 Prob(JB): 0.00
Kurtosis: 63.084 Cond. No. 3.75e+16


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 2.94e-28. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.

Model Analysis- Evaluation of the model¶

Testing the Assumptions¶

In [ ]:
## Linearity
In [270]:
errors= y_test-pred_y
In [271]:
residual= model1_rs_ols_test.resid
In [272]:
errors.describe()
Out[272]:
count    4.323000e+03
mean     4.840964e+03
std      2.194469e+05
min     -1.307021e+06
25%     -9.464312e+04
50%     -7.553444e+03
75%      8.106587e+04
max      4.436541e+06
Name: price, dtype: float64
In [273]:
residual.describe()
Out[273]:
count    4.323000e+03
mean     5.458567e-11
std      2.160893e+05
min     -1.244321e+06
25%     -1.035952e+05
50%     -5.831742e+03
75%      8.743283e+04
max      3.911706e+06
dtype: float64
In [290]:
from sklearn.metrics import mean_absolute_error,mean_absolute_percentage_error,mean_squared_error
In [291]:
##performance metrices : MAE, MAPE,MSE,RMSE  
mae = mean_absolute_error(y_test, pred_y)
mape= mean_absolute_percentage_error(y_test, pred_y)
mse= mean_squared_error(y_test, pred_y)
rmse= mean_squared_error(y_test, pred_y, squared=False)
print(mae, mape,mse,rmse)

127619.31428621049 0.25426683229434555 48169231013.253395 219474.8983671103
In [ ]:
In [ ]:
In [ ]:
In [281]:
sns.scatterplot(x=pred_y,y=errors)
Out[281]:
<AxesSubplot:ylabel='price'>
  1. No linearity
  2. Hetroskedasticity
  3. No normality
  4. impact of outliers
In [278]:
sns.scatterplot(x=y_test,y=errors)
Out[278]:
<AxesSubplot:xlabel='price', ylabel='price'>
In [280]:
sns.scatterplot(errors, y_test)

C:\Users\mallikarjunad\Anaconda3\lib\site-packages\seaborn\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
Out[280]:
<AxesSubplot:xlabel='price', ylabel='price'>
In [283]:
dfn.columns
Out[283]:
Index(['price', 'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'waterfront', 'view', 'condition', 'grade', 'sqft_above', 'sqft_basement', 'zipcode', 'lat', 'long', 'sqft_living15', 'sqft_lot15', 'renovated_status', 'house_age'], dtype='object')
In [285]:
dfn_numeric= dfn[['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 
             'sqft_above', 'sqft_basement', 'zipcode', 'lat', 'long', 
              'sqft_living15', 'sqft_lot15', 'house_age']]
In [287]:
features= dfn_numeric.columns
In [286]:
dfn_numeric.head()
Out[286]:
bedrooms bathrooms sqft_living sqft_lot floors sqft_above sqft_basement zipcode lat long sqft_living15 sqft_lot15 house_age
0 0.0 -1.666667 -0.650045 -0.348442 -0.5 -0.372549 0.000000 1.329412 -0.292754 -0.133005 -0.574713 -0.395344 0.422222
1 0.0 0.000000 0.587711 -0.066572 0.5 0.598039 0.714286 0.705882 0.720773 -0.438424 -0.172414 0.003813 0.511111
2 -1.0 -1.666667 -1.015138 0.421742 -0.5 -0.774510 0.000000 -0.435294 0.802415 -0.014778 1.011494 0.088702 0.933333
3 1.0 1.000000 0.044524 -0.463527 -0.5 -0.500000 1.625000 0.835294 -0.246377 -0.802956 -0.551724 -0.525788 0.200000
4 0.0 -0.333333 -0.204809 0.081799 -0.5 0.117647 0.000000 0.105882 0.217391 0.911330 -0.045977 -0.023480 -0.266667
In [288]:
from statsmodels.stats.outliers_influence import variance_inflation_factor
vif= pd.DataFrame()
vif['VIF_values']= [variance_inflation_factor
                    (dfn_numeric.values,i)for i in range(dfn_numeric.shape[1])]
vif['features']= features
In [289]:
vif
Out[289]:
VIF_values features
0 1.596240 bedrooms
1 3.257688 bathrooms
2 19.831971 sqft_living
3 2.098121 sqft_lot
4 1.979021 floors
5 14.704394 sqft_above
6 4.041223 sqft_basement
7 1.626079 zipcode
8 1.134831 lat
9 1.769884 long
10 2.629139 sqft_living15
11 2.132832 sqft_lot15
12 1.884200 house_age

since only 2 features : ' sqft_above' and sft_living are having high VIF values, driop these columns rebuild the model.